Realization of any finite jet in a scalar semilinear parabolic equation on the ball in ${ℝ}^{3}$
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 18 (1991) no. 1, p. 83-102
@article{ASNSP_1991_4_18_1_83_0,
author = {Pol\'a\v cik, Peter},
title = {Realization of any finite jet in a scalar semilinear parabolic equation on the ball in $\mathbb {R}^3$},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
publisher = {Scuola normale superiore},
volume = {Ser. 4, 18},
number = {1},
year = {1991},
pages = {83-102},
zbl = {0774.35041},
mrnumber = {1118222},
language = {en},
url = {http://www.numdam.org/item/ASNSP_1991_4_18_1_83_0}
}

Poláčik, Peter. Realization of any finite jet in a scalar semilinear parabolic equation on the ball in $\mathbb {R}^3$. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 18 (1991) no. 1, pp. 83-102. http://www.numdam.org/item/ASNSP_1991_4_18_1_83_0/

[Am] H. Amann, On abstract parabolic fundamental solutions, J. Math. Soc. Japan, 39 (1987), 93-116. | MR 867989 | Zbl 0616.47032

[Be] M.S. Berger, Nonlinearity and Functional Analysis, Academic Press, New York 1977. | MR 488101 | Zbl 0368.47001

[Bi] Y.N. Bibikov, Bifurcation of invariant tori for systems with degeneracy, (in Russian), in: Questions of The Qualitative Theory of Differential Equations, V.M. Matrosov and L.Y. Anapolskii (eds.), Nauka, Novosibirsk 1988, 1-23.

[Ch-H] S.N. Chow - J.K. Hale, Methods of Bifurcation Theory, Springer-Verlag, New York 1982. | MR 660633 | Zbl 0487.47039

[Co-H] R. Courant - D. Hilbert, Methods of Mathematical Physics, Interscience, New York 1953. | MR 65391 | Zbl 0051.28802

[Da 1] E.N. Dancer, The effect of domain shape on the positive solutions of certain nonlinear equations, J. Differential Equations 74 (1988), 120-156. | MR 949628 | Zbl 0662.34025

[Da 2] E.N. Dancer, On the existence of two-dimensional invariant tori for scalar parabolic equations with time periodic coefficients, preprint.

[F-P] B. Fiedler - P. POLÁčIK, Complicated dynamics of a scalar reaction diffusion equation with a nonlocal term, Proc. Roy. Soc. Edinburgh, 115A (1990), 167-192. | MR 1059652 | Zbl 0726.35060

[G-S] M. Golubitski - D. Schaeffer, Singularities and Groups in Bifurcation Theory, Appl. Math. Sci. 51, Springer-Verlag, New York 1986. | Zbl 0607.35004

[Ha 1] J.K. Hale, Flows on centre manifolds for scalar functional differential equations, Proc. Roy. Soc. Edinburgh, 101A (1985), 193-201. | MR 824220 | Zbl 0582.34058

[Ha 2] J.K. Hale, Local flows for functional differential equations, Contemp. Math. 56, Amer. Math. Soc., Providence 1986, 185-192. | MR 855090 | Zbl 0612.34066

[He] D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math., 840, Springer-Verlag, New York 1981. | MR 610244 | Zbl 0456.35001

[Ka] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin 1966. | MR 203473 | Zbl 0148.12601

[Ma] H. Matano, Convergence of solutions of one-dimensional semilinear parabolic equations, J. Math. Kyoto Univ. 18 (1978), 221-227. | MR 501842 | Zbl 0387.35008

[Po 1] P Poláčik, Convergence in smooth strongly monotone flows defined by semilinear parabolic equations, J. Differential Equations 79 (1989), 89-110. | MR 997611 | Zbl 0684.34064

[Po 2] P Poláčik, Domains of attraction of equilibria and monotonicity properties of convergent trajectories in semilinear parabolic systems admitting strong comparison principle, J. Reine Angew. Math., 400 (1989), 32-56. | MR 1013724 | Zbl 0667.35036

[Po 3] P Poláčik, Complicated dynamics in scalar semilinear parabolic equations in higher space dimension, J. Differential Equations, 89 (1991), 244-271. | MR 1091478 | Zbl 0738.35027

[Po 4] P Poláčik, Imbedding of any vector field in a scalar semilinear parabolic equation, Proc. AMS, to appear. | MR 1089411 | Zbl 0755.35046

[Sm] V.I. Smirnov, A Course of Advanced Mathematics III2, Nauka, Moscow, 1974. | MR 361650

[Ta] P Takáč, Domains of attraction of generic w-limit sets for strongly monotone semiflows, Z. Anal. Anwendungen, to appear. | MR 1155611 | Zbl 0764.58019

[Tr] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North Holland, Amsterdam 1978. | MR 503903 | Zbl 0387.46032

[Va] A. Vanderbauwhede, Local Bifurcation and Symmetry, Research Notes in Mathematics, Pitman, Boston 1982. | MR 697724 | Zbl 0539.58022

[Ze] T.J. Zelenyak, Stabilization of solutions of boundary value problems for a second order parabolic equations with one space variable, Differential Equations 4 (1968), pp. 17-22. | MR 223758 | Zbl 0232.35053